Remark 6.9 One can decide if a nontrivial \(M\)  of a given order exists in the centralizer of \(L_4\) , we computed it through a Grünbaum approach [1]} (solving \([L_4,M]=0\)  directly), see examples in Section REF . For certain families of operators in the Weyl algebra \(\mathcal {C}(L_4)\ne {\bf C}[L_4]\)  it is guaranteed in [2]}, [3]}, [4]}, [5]}, [6]}, see also [7]}.

